Master of Science Thesis

Digital Tomosynthesis: Fundamental principles and

comparison to conventional X-ray imaging

Christian Bernhardsson

Supervisor: Anders Tingberg, PhD

The work has been performed at Department of Radiation Physics

Malmö University Hospital

Medical Radiation Physics Clinical Sciences, Lund

Lund University, 2006

CONTENTS 1

Contents

1 Introduction 1

1.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.1 Geometrical tomography . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.2 Tomosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Purpose of the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Material and methods 6

2.1 Phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Image acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Post-processing of the image data . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Tomographic parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.5 Tomosynthesis compared to conventional X-ray imaging . . . . . . . . . . . . 11

2.5.1 Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.5.2 Anthropomorphic phantom . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Results 12

3.1 Tomographic parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2 Tomosynthesis compared to conventional X-ray imaging . . . . . . . . . . . . 13

3.2.1 Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2.2 Anthropomorphic phantom . . . . . . . . . . . . . . . . . . . . . . . . 18

4 Discussion 20

5 Conclusions 22

6 Acknowledgements 22

Abstract

During the last century several attempts have been made to overcome the fundamentalproblem of X-ray imaging, i.e. that anatomical information existing in 3-dimensions hasto be represented on a 2-dimensional radiograph. In this thesis, digital tomosynthesis, are�ned version of conventional tomography, has been investigated. Digital tomosynthesisenables retrospective reconstruction of an arbitrary plane in the imaged patient from a seriesof low dose projections, acquired with a limited tube movement. In the simplest method ofreconstructing arbitrary planes, all the projections are shifted such that structures from onlyone plane line up exactly and thus remain �xed relative to the over- and underlying structures.To investigate the fundamental principles of tomosynthesis and evaluate the clinical potentiala prototype was built. Quality metrics such as signal di�erence to noise ratio (SDNR) andartifact spread function (ASF) were measured with di�erent tomographic parameter settings.The tomosynthesis acquisition parameters were optimized and the image quality at di�erentexposure levels were compared to conventional radiographs. The optimization evaluationshowed that a large angular range with many projections can increase the image quality andreduce artifacts created from surrounding anatomy. It was also shown that small and obscuredobjects were easier to discern with tomosynthesis compared to conventional X-ray imaging,even at lower exposures. Reconstructed images of an anthropomorphic chest phantom showedan increased visibility of local structures in the lungs, structures which becomes superimposedon surrounding anatomy in a conventional X-ray image. These results are a consequence ofthe intrinsic property of tomosynthesis; each image, reconstructed from a series of projections,have high signal from in-focus objects and low signal from the surrounding anatomy that isrepeated over the image proportional to the number of projections. The ability to separatethe surrounding anatomy from the in-focus structures can be optimized with the appropriatecombination of angular range and the number of projections acquired.

1 INTRODUCTION 1

1 Introduction

The X-ray modalities clinically available today include 2-dimensional imaging (i.e. pla-nar imaging, geometrical tomography, mammography, angiography and �uoroscopy) and3-dimensional imaging (computed tomography, CT). In a conventional X-ray image all struc-tures in the imaged 3D volume become superimposed onto a 2D radiograph. This can decreasethe ability for the radiologist to detect pathologies and therefore lead to inaccurate diagnoses.Geometrical tomography is limited to high-contrast imaging [1] but is a low cost alternativeto CT and reduces the confusion of over- and underlying structures by focusing on one speci�cplane. In geometrical tomography the entire thickness of the patient is exposed to acquire asingle tomogram (slice). If several slices are needed to locate the lesion, multiple exposuresare required and the dose to the patient will increase proportional to the number of slicesacquired. The 3D imaging modality, CT, is a complex X-ray technique that utilizes the ideasof tomography with the aid of computers to make 2D slices of 3D objects. CT images hasundoubtedly led to signi�cant advances in patient care, although high levels of patient doseare involved and it is expensive to implement.

In this paper another X-ray modality will be investigated, namely digital tomosynthesis.This is a 3D imaging technique that has the ability to address some of the shortcomingsof the other X-ray modalities. Digital tomosynthesis reduces the confusion of superimposedstructures and allows retrospective reconstruction of an arbitrary number of tomographicplanes, at a lower cost and lower dose than CT.

The principles of tomosynthesis are not new but have evolved from geometrical tomography.Geometrical tomography [2] was �rst implemented by Ziedses des Plantes 1932 after severalother attempts [3]. Not until 1969 when Garison et al. made a successful experiment [4] the�rst tomosynthesis images were seen. Since the pioneers were using �lm-based systems [5][6], the post processing of the images was limited. Another disadvantage which did not maketomosynthesis clinically acceptable in the beginning was the lengthy procedure with a �lmchange between each exposure. To shorten the tomosynthesis acquisition time video camerascoupled to an image intensi�er screen and a television display were utilized [7]. Later theanalogue video cameras became digital with the introduction of the charge-coupled device(CCD). Then it was possible to acquire higher quality X-ray images and store them digitally.The only problem left was the lack of computational power needed for the reconstruction. Inthe late 1970s the introduction of tomosynthesis as a new modality seemed to have failed,when CT became widely accepted. The further development of tomosynthesis was then slowuntil the late 1990s when rapid digital �at-panel detectors became available and the cost ofcomputing the tomosynthesis reconstruction and post-processing routines dropped. Thesetechnological advancements started a new interest in re�ning and developing tomosynthesis.

For a dedicated tomosynthesis equipment there are a few requirements that must be ful�lled;

• A large area digital detector capable of fast readout

• Because each exposure is low dose it is essential that the image receptor has a highdetective quantum e�ciency with low quantum- and electronic noise

• The system must be able to handle fast movement of the tube, in small and preciseangle increments

• A fairly fast computer with reconstruction software

Today, detectors that ful�ll these conditions are available and a tomosynthesis study can be

1 INTRODUCTION 2

performed very fast, the whole series of projections can be acquired within a single breathhold[8] [9] (chest imaging). Tomosynthesis prototypes have been developed for mammography[10] and chest imaging [11] but several other imaging tasks are also investigated i.e. an-giography, urography, images of inner ear, orthopedic, �nger joints and dental applications[12]. Apart from clinical implementations of tomosynthesis much of the research is concen-trated on developing new reconstruction algorithms and methods to reduce the blurring fromout-of-plane structures. In this paper the fundamental properties of tomosynthesis as a newmodality will be investigated. This includes parameters that will a�ect the �nal slices and acomparison to conventional X-ray imaging.

1.1 Theory

In conventional planar X-ray imaging there are a few factors that limit the ability to visualizestructures, especially when they are small and obscured. One of the most fundamental factorsis that objects in the imaged 3D volume become superimposed on the 2D radiograph. Thedata in each pixel is related to the sum of the di�erent attenuation coe�cients along thebeam through the object, see equation 1. This will lower the contrast and make it di�cult,or even impossible, to detect subtle anomalies. Another di�culty in planar imaging is thatthe spatial distribution of objects is obscured. This geometrical e�ect makes it hard to drawconclusions about the shape and relative position of various structures. A third factor, whichcontradictively is the factor that give rise to the contrast in the X-ray images, might alsodecrease the diagnostic information, is caused by attenuation e�ects. This e�ect arises fromthe fact that the incident X-ray intensity, I0, reduces to I when striking the detector dueto attenuation of the di�erent organs. If a narrow beam of monoenergetic photons with aninitial transmitted intensity, I0, penetrating several tissues, i, of di�erent thickness, xi, andattenuation coe�cients, µi, the intensity striking the detector, I, is given by the equation:

I = I0 · e−P

i µixi (1)

From this equation it is easy to see that the beam attenuation, I/I0, depends on both µ andx. This can cause uncertainties when comparing two structures that appears to be similarin an image. The structures might appear similar but can be composed of di�erent tissueswith di�erent thickness since a di�erence in attenuation can be due to changes in thickness,composition or a combination of both.

1.1.1 Geometrical tomography

One method to overcome the previously described problems is with geometrical tomography,also called body tomography or conventional tomography. This method utilizes geometricalfocusing techniques to achieve the tomographic e�ect. The word "tomography" comes fromthe Greek tomos (slice) and graphia (picture). The aim of tomographic imaging is to get ahigh contrast in one speci�c plane, the 'focal plane' or 'plane of cut', of the imaged objectand blur out object structures outside of this layer. This can be accomplished by movingthe tube and the detector, during a continuous emission of X-rays, provided that the middleof the tube always points at a speci�c position on the detector. The most common way toachieve this is to use a parallel-path geometry and move the tube and detector in a linearfashion, in opposite directions, as in �gure 1.

1 INTRODUCTION 3

♥

Movement of tube

Movement of detector

Plane of movementof X-ray tube

Plane of movement of detector

Focal planeOverlying plane (structures)

♥■

Figure 1: An illustration of linear tomography. When the exposure begins the tube istilted, typically 20◦, from the normal to the detector. During the exposure, continuousreinforcement of the structures in the focal plane (♥) is achieved while structures abovethis plane (�) is smeared out from right to left across the detector.

To do a geometrical tomography a focal plane must be selected, which will be the fulcrumof the system and this plane will determine the di�erent speeds1 of the tube and detectorduring the exposure. During the movement, continuous reinforcement of the focal plane isachieved while structures from over and underlying planes are blurred out due to parallax,proportional to their distance from the focal plane. Hence, in this geometry all objects in thefocal plane will be projected to the same location on the detector and therefore, they appearto be stationary.

Since the out-of-plane anatomy of the patient is not e�ciently removed from the image, to-mographic images tend to be inherently low in contrast. Therefore, conventional tomographyis used for high-contrast situations only, such as urography with contrast agents and imagingof the inner ear where the contrast is high between air to bone [1]. Another disadvantage isthat only one plane per exposure can be set as the focal plane.

1When the focal plane is set in the middle of the X-ray tube and the detector, the tube

and detector will move with the same speed and distance to the image volume.

1 INTRODUCTION 4

1.1.2 Tomosynthesis

Tomosynthesis is similar to conventional geometrical tomography in that it uses the samegeometry, the di�erence is the synthesis of the images. In tomosynthesis a sequence ofprojection radiographs are acquired during a single motion of the X-ray tube. These di�erentradiographs allows for an arbitrary number of in-focus planes to be generated retrospectively.There are a few di�erent geometrical con�gurations available for tomosynthesis [13] and themethod proposed here is based on a linear movement of the tube-detector system.

In linear tomosynthesis the X-ray tube and detector move in opposite directions parallelto the fulcrum plane, see �gure 2. Several low dose exposures are acquired during themovement from 1 to 3 and the tomographic angle (or angular range), φ, typically varies from-20≤ φ ≤20 degree in intervals of about ∆φ = 2 degree, depending on the examination andsystem capabilities. The angle is from the perpendicular to the detector and the synchronousmovement depends on where the fulcrum plane is situated (plane B in �gure 2).

Movement of tube

Movement of detector

Plane of movementof X-ray tube

Plane of movement of detector

Fulcrum plane (B)Tomographic plane (A)

♥■

♥ ■♥■

H

h

h

x x

1 2 3

♥

Figure 2: Illustration of the tube and detector movement during the tomographicmotion (only three exposures are shown for simplicity). Plane B is the fulcrum planeseparated ∆h from the overlying plane, A. At the outermost projections (1 and 3)the object in plane A is displaced a speci�c amount ∆x from the underlying object inplane B.

As in geometrical tomography the image structures in one plane are enhanced, the focal plane,and objects outside of this plane are blurred out if the di�erent projections are just added.However, with a reconstruction method any plane through the volume can be set as the focal

1 INTRODUCTION 5

plane, retrospectively. Several methods have been proposed for suppressing nonrelevant planeinformation and enhancing the image quality [14] - [18] but the most common is the so called'Shift-And-Add' method [5] �rst proposed by Grant.

The Shift-And-Add method is akin to (un�ltered) backprojection and takes into considerationthat objects at di�erent heights above the detector will experience di�erent degrees of parallaxas the tube moves. When using linear geometry, the tube and detector move in synchrony inparallel planes so that the magni�cation of objects depends only on their height above thedetector, not on the location of the tube or detector within these two planes. When theseconditions are ful�lled it is possible to shift and add the di�erent images to bring a speci�cplane into focus. During the �rst step, the images are shifted. The amount of shift, ∆x,depends on the position of, and height above the detector. Consider the triangles createdby the rays in �gure 2. It is easy to se that the sides opposite to φ

2 (parallel to the plane ofmovement of the tube) is given by

∆h · tanφ

2+ h · tan

φ

2and h · tan

φ

2(2)

for the two smaller triangles and

∆x + H · tanφ

2and H · tan

φ

2(3)

for the other two. By similar triangles, the ratios of these sides must be equal, we get

∆h · tan φ2 + h · tan φ

2

h · tan φ2

=∆x + H · tan φ

2

H · tan φ2

(4)

The exact length of the shift, ∆x, can then be calculated by regrouping eq. 4:

∆x =H ·∆h · tan φ

2

h(5)

were H is the focus-to-detector distance, h the distance from the tomographic plane (i.e.in-focus plane) and the tube, ∆h the distance between the fulcrum- and tomographic plane(the plane to reconstruct) and φ is the tomographic angle. The projections are then addedwith the right amount of shift applied, so that the structures in plane A are all made to lineup exactly and thus be in focus. In �gure 3 the principles of the Shift-And-Add method isillustrated for the speci�c case in �gure 2.

1.2 Purpose of the study

The purpose of this study was to evaluate the clinical potential of tomosynthesis and inves-tigate if it was possible to obtain more information for a certain situation than conventionalX-ray imaging at the same or even smaller dose. To determine this the di�erent parame-ters associated with the acquisition and reconstruction processes had to be investigated andoptimized.

2 MATERIAL AND METHODS 6

♥■

♥■

■♥

■ ♥

■♥■■

♥♥

■ ♥

■

■

♥♥

■

♥

■♥1

+2

+3

=Plane B Plane A

Figure 3: Tomosynthesis reconstruction method Shift-And-Add with three di�erentprojections. The focal plane (B) is brought to focus simply by adding the projections.Plane A is reconstructed by shifting the bilateral projections the same amount andadding them together with the middle projection.

2 Material and methods

The clinical interest in tomosynthesis is increasing but no dedicated system was available atMalmö University Hospital when this project was performed. Therefore, existing equipmentwas used to build a prototype, which included a Varian X-ray tube with a Canon CXDI(a-Si) digital �at panel detector and a computer. The Canon CXDI utilized a Large AreaNew MIS Sensor and TFT (LANMIT) with an image matrix of 2688×2688 pixels and a pixelpitch of 160 µm. The detector had a read-out of 0.3 seconds [20], which was considerablyshorter than the time between each X-ray exposure (∼20 seconds).

The X-ray equipment was located at the urography section of the Radiology Departmentwhere the systems are capable of geometrical tomography. Hence, it was possible to use thegeometrical con�guration described in �gure 1, however the X-ray unit was limited to anangular range of 60◦ (±30◦). Since the system software only used the radiated part of thedetector, each projection had a di�erent matrix size. This is unacceptable when shifting andadding the projections since there is no �xed reference point. Thus, the system was modi�edby adjusting the software and force it to use a �x detector matrix for each projection. Forevery measurement a 2688×2688 pixel matrix was used with a 45×45 cm FOV, which wasnecessary because of the large phantoms used.

2 MATERIAL AND METHODS 7

2.1 Phantoms

The phantoms used in the study included an abacus-like physical phantom (see �gure 4) andan anthropomorphic chest phantom. The physical phantom was used to study the impactof di�erent tomographic parameters on the reconstructed slices and in a comparative studywith conventional X-ray imaging. The anthropomorphic chest phantom was investigatedwith both tomosynthesis and conventional X-ray imaging to compare the diagnostic valuebetween the modalities.

The physical phantom frame is made of plexiglas (PMMA) and has the exterior dimensions:300×190×140 mm. Inside the phantom there are several nylon strings (diameter of 1.5 mm)attached to the frame. The strings are placed to build up 4 di�erent planes with 4 stringsper plane. These planes will be refereed to as the "natural planes" to avoid confusion. Theinterspacing between the natural planes and also between the bottom of the phantom tothe �rst plane is 30 mm. Spheres and ellipsoids of various sizes are attached to the strings(diameter of 30, 20, 15, 10, 7 and 5 mm). The spheres are made of polypropylene (ρ = 0.910g/cm3) and the ellipsoids of PMMA (ρ = 1.190 g/cm3). To make the situation more realisticthe phantom was �lled with water. This small di�erence in density, compared to water (ρ ≈1 g/cm3), made the phantom optimal for a comparison study of conventional X-ray imagingand tomosynthesis.

a

b

c

Figure 4: The physical phantom seen from; a) the side, b) above and c) below.

2.2 Image acquisition

In the physical phantom the di�erent spheres and ellipsoids were movable. This made itpossible to move and place di�erent sized objects at interesting positions. In table 1, objectsat the same position parallel to the detector plane (XY-plane) but di�erent positions in the Z-direction are listed. These positions were chosen to obtain almost every possible arrangement

2 MATERIAL AND METHODS 8

of the objects (overlying/underlying, size, composition, distance) and this con�guration wasutilized during the entire study. Since this will generate a large amount of data only some ofthe objects were investigated in close detail.

Table 1: The position of the spheres and ellipsoids in the di�erent planes of thephantom. Each row in the table represents objects at the same XY-position but atheights above the table (Z-position).

Object Size/mm Depth/mm Over-/Underlying object Size/mm Depth/mm

PMMA 15 30 Polyp. 15 120PMMA 20 30 Polyp. 20 90PMMA 30 30 Polyp. 30 120Polyp. 5 30 PMMA 7 90Polyp. 20 30 PMMA 30 90PMMA 7 60 Polyp. 20 120PMMA 30 60 Polyp. 15 120PMMA 20 90 Polyp. 10 120PMMA 10 90 Polyp. 10 120

Each acquisition was performed in the same manner. The phantom was placed on the table inthe middle of the X-ray �eld, which was maximized (45×45 cm) to cover the entire phantomfor every angle. The fulcrum plane (i.e. pivot for the movement of the tube and detector) wasselected with a laser positioning system attached to the wall and coupled to the X-ray unit.This plane was selected in the middle of the phantom, 185 mm above the detector. When thepositioning of the fulcrum plane was satisfactory, the phantom was �lled with water (approx.9.5 liters) and the position on the table adjusted, if it was necessary. Finally, the X-ray tubesettings were con�gured and the acquisition could start. During the acquisition the X-raytube was moved manually between each exposure and the precision of the angles depended onthe built-in measuring device. A separate inclinometer was used to improve the accuracy ofthe measured angles from the built-in device to a precision of ±1◦. Nevertheless, the accuracyof the angles is not a crucial factor due to the inherent properties of the reconstructionmethod.

Because objects outside the slice of interest will appear as blurring artifacts in the tomosyn-thesis images and become superimposed on the conventional radiographs a CT study wasalso performed. Images reconstructed with a CT only contain information from the exposedslice, these images will therefore serve as a reference when comparing tomosynthesis to con-ventional X-ray imaging. For this purpose a Siemens Somatom Sensation 64 was utilized. Athorax routine protocol with 120 kV, 100 mAs and 3.2 mm slice thickness was used in thisstudy. Since the reconstructed images were slices perpendicular to the table a special recon-struction program, In-space [21] had to be utilized. In-space o�ers the ability to reconstructand view any plane throughout the imaged volume. With this tool the four natural planesof the phantom were located and saved, see �gure 5.

2.3 Post-processing of the image data

After each acquisition the images were stored in the Picture Archiving and CommunicationsSystems (PACS) and downloaded to a PC (P4 3.0 GHz and 1 Gb RAM) were the reconstruc-

2 MATERIAL AND METHODS 9

tion was performed. The tomograms were synthesized from the projections with a software,based on the shift-and-add method, written in IDL [22]. The projections were not linearized(logarithmic transformed) prior to the reconstruction. A nonlinear relationship may be usedto reconstruct images but will not be capable of removing blur from the images with de-blurring algorithms. Here the tomosynthesis images were studied without such algorithmsand therefore the blur in the images is determined by the tomographic parameters and theexposure will not be linearly related to the response on the detector.

In the tomosynthesis process there are a few variables in the reconstruction program thatwill a�ect the quality of the �nal slices. Therefore, some of the parameters together with themain parts of the program will be described.

During image acquisition, the projection of the object onto the detector moves/shifts laterallyas the detector and X-ray source are moved with respect to each other. To reconstruct theobject, the projection images are shifted with respect to each by incremental amounts andsummed to obtain slices through the object. In order to avoid exceeding the dimensions ofthe detector �eld-of-view while shifting the images, a central region of interest is selected fromthe detector array. This region is restricted by an upper- and a lower limit, in the directionof the tube movement, determined by the total matrix height, number of slices necessary tocover the whole volume, the shift factor and which image that represented the 0◦-projection.

Each of the projection images was read sequentially into the reconstruction program, with the0◦-projection (AP) in the middle. These were then rebinned to 672×672 pixels (1/16 of theoriginal), to save computational time and a central region of interest selected, as describedabove. Each of the re-scaled images (except the one in the middle) were shifted and addedto create a 3D volume of the slices. The speci�c amount of shift applied to the di�erentprojections depends on two factors; 1) the projection to shift and 2) the wanted in-focusplane. To create slices of the imaged volume from the series of projections a �xed shift factorwas introduced, which typically varied between 0.05 to 0.2 pixels and determines the distancebetween two adjacent slices. Depending on the reconstruction depth (or the wanted in-focusplane) the shift factor was weighted accordingly to the two factors above. In this way it ispossible to generate an unlimited number of slices, for a given series of projections. However,the resolution will not increase in�nitely but will be restricted by the point-spread function(PSF) of the system.

When all of the projection images had been shifted and added to bring a speci�c plane intofocus the new images, i.e. slices, were stored as .ti� �les (16-bit grayscale) for analysis withan image viewer. To �nd the right planes for investigation, a volume rendering was createdwhich gave a gross estimate on where the slices were cutting the phantom. For each situationevery third slice were stored and when the best in-focus slice was located among these, theclosest over- and underlying planes were studied further.

2.4 Tomographic parameters

The �rst investigation was to determine how the tomographic parameters a�ect the recon-structed slices. The examined parameters included the tomographic angle, φ, angle incre-ment between each projection, ∆φ, and the number of acquired projections, NAcq. Because

NAcq = φ∆φ + 1 it is impossible to �x two of them and vary the third. Therefore the study of

the tomographic parameters was divided into three cases. For each case a speci�c parameterwas �xed to cover all possible situations. The settings used for each case is listed in table 2.

2 MATERIAL AND METHODS 10

When the phantom was placed on the table and �lled with water, the X-ray tube settingswere con�gured. This was done by changing kilovoltage and mAs to get a good image qualityin a 0◦ AP-projection. At 60 kVp and 105 mAs the signal from the di�erent objects was highenough to discern most of the objects in the phantom. The tube loading were then dividedamong the projections in the tomosynthesis series so that the total exposure was the same.

When all projections in the series were acquired a 3D volume was reconstructed using asoftware written in IDL and slices cutting the natural planes of the phantom were saved.The quality of the images were evaluated by both a visual comparison and measurement ofthe signal di�erence to noise ratio (SDNR) for six of the smallest objects in the phantom.The measurements were made in the middle of the objects and in the adjacent background.In order to do the comparison more consequent ROIs were placed so that no part of themwere located in an artifact. The SDNR is a measure of the detectability of an object in areconstructed plane and is de�ned by

SDNR =µ̄object − µ̄BG

σBG(6)

were µ̄object is the mean pixel intensity of the object, µ̄BG is the mean intensity of the imagebackground, and σBG is the standard deviation of the homogenous background pixel intensitycalculated in a large ROI with ImageJ [23]. The ROIs were placed at the same position inthe objects and in the image background so that no part of the ROIs were located in anartifact.

When the di�erent parameters associated with the acquisition vary, artifacts caused by over-and underlying structures will also vary. The artifacts appear as blur in the reconstructedslices and will reduce the diagnostic value of the images. To quantify the magnitude of theblur an artifact spread function (ASF) [24] was utilized. This is an extension of the PSFwhich is a measure of the spread of signal of a point. The ASF is a measure of the intensityof the artifact relative to the intensity of the (real) object causing the artifact. Another wayto interpret the ASF is the capability of tomosynthesis in di�erentiating objects that aresuperimposed along the Z direction, the direction perpendicular to the reconstruction plane(XY). The ASF is de�ned by

ASF (z) =µ̄artifact(z)− µ̄BG(z)µ̄object(z0)− µ̄BG(z0)

(7)

were µ̄artifact(z) and µ̄BG(z) are the mean pixel intensities of the artifact and the backgroundin the o�-focus plane z, µ̄object(z0) and µ̄BG(z0) are the mean pixel intensities of the objectand the image background in the in-focus plane z0, respectively. The ASF was measuredfor the 30 mm polypropylene sphere located at plane 4 (z0 = 120 mm above the table).µ̄object(z0) was measured with a ROI placed over the (real) object in plane four and a ROIin the image background measured µ̄BG(z0). In every fourth plane, between plane 4 to plane

Table 2: Parameter settings for the investigation of the tomographic parameters.

Case φ ∆φ NAcq

1 20◦, 40◦, 60◦ 2◦, 4◦, 6◦ 112 40◦ 2◦, 4◦, 5◦, 21, 11, 93 20◦, 40◦, 60◦ 2◦ 11, 21, 31

2 MATERIAL AND METHODS 11

1 at z = 30 mm above the table, the intensity of the artifact (the numerator in equation 7)was measured. The ROI to measure µ̄artifact(z) was placed over the region of the artifact atthe same position in all of the slices and with the same area. The image background in theo�-focus planes, µ̄BG(z), was measured with a ROI outside the artifact.

2.5 Tomosynthesis compared to conventional X-ray imaging

2.5.1 Exposure

To do a comparison study between the modalities, images acquired with the conventionaltechnique were compared to tomosynthesis images acquired with the same mAs and kVp. Five0◦-projections or anterior-posterior (AP) projections were acquired at 60 kVp and di�erentmAs. The tomosynthesis examination were performed with the same, or as close as possibleto the total exposure (mAs), of the conventional AP. The tomosynthesis examination (TS)included 11 projections over an angular range of 40◦. In table 3 the di�erent settings for eachcomparison are listed.

Table 3: The di�erent mAs settings for the AP and the associated TS projections.For each case the di�erence of the total mAs between the methods are listed, with APprojection as reference.

Study Conventional/mAs mAs per tomosynthesis proj. Total di�erence/%

1 32 3.1 102 64 6.2 63 128 12.5 104 252 20.0 -85 400 32.0 -8

When comparing the �ve studies, three di�erent objects within the phantom were selected.These included a 15 mm PMMA ellipsoid (z = 30 mm above the table), a 20 mm polyprophy-lene sphere (z = 30 mm above the table) and a 10 mm polyprophylene sphere (z = 120 mmabove the table). The objects were selected since they were the smallest objects visible in allof the images and had di�erent properties (size, composition, over-/underlying structures).At each mAs-setting the SDNR were measured for these three objects and compared betweenthe techniques.

2.5.2 Anthropomorphic phantom

To investigate the clinical bene�ts of tomosynthesis an anthropomorphic chest phantom wasstudied with conventional radiography and tomosynthesis. The phantom was positioned inan AP view mode and the scanning direction along the spine with an angular range of 20◦

and 2◦ steps. A conventional chest image is typically acquired with 140 kVp and 2 mAs butit was not possible to generate such high kVp/mAs ratio due to the tube rating, therefore100 kVp and 3.2 mAs were used instead.

To de�ne the location of the slices, two �ducial markers were placed on a ruler at di�erentpositions above the table, zup = 150 mm and zlow = 50 mm and there were Nrecon recon-structed slices evenly spread between zup and zlow. The reconstructed planes were located

3 RESULTS 12

at zi = zlow + i ·∆z, were 0 6 i 6 Nrecon − 1 and ∆z is a measure of the distance betweenthe slices, de�ned by

∆z =zup − zlow

Nrecon − 1(8)

The clinical information obtained from the tomosynthesis acquisition was visually comparedto that from the conventional.

3 Results

As reference or gold standard, images of the physical phantom acquired with CT are enclosedin �gure 5. In these images it is possible to see all of the structures in the phantom as wellas the nylon strings.

Plane 1, z = 30 mm

Plane 3, z = 90 mm Plane 4, z = 120 mm

Plane 2, z = 60 mm

Figure 5: The four natural planes of the physical phantom acquired with CT. Becausethe objects within the physical phantom were loose there are some small di�erencesbetween the tomosynthesis slices and the CT slices although the objects positions inthe Z-direction are retained.

3.1 Tomographic parameters

Some illustrative examples from the di�erent cases are shown in �gure 6. As the angularrange increases, out-of-plane objects are smeared over a larger area and therefore appear withdiminished intensity compared with objects in focus. This e�ect is possible to see in �gure 6where the smeared object is marked with an arrow.

The images acquired with the conventional technique and tomosynthesis were compared andthe SDNR was measured for some of the smallest objects in the phantom, see �gure 7. Alarge angular range seems to lower the SDNR and in some of the images it was not possibleto see the objects (with φ = 60◦). Figure 7C indicate that a large number of projections

3 RESULTS 13

a b c

Figure 6: Examples of plane 1 in the physical phantom, reconstructed from projec-tions acquired with; a) φ = 20◦ and ∆φ = 2◦, b) φ = 40◦ and ∆φ = 4◦, c) φ = 60◦

and ∆φ = 6◦. Objects in overlying planes becomes more smeared out (marked withan arrow) when φ and ∆φ increases. This increases the visibility of the structures inthe in-focus plane. Note that the images have di�erent sizes due to the increase innumber of shifts, not the increase in angle.

with a small angular range will improve the SDNR. In �gure 7B it is not possible to seeany relationship between ∆φ and the SDNR when the angular range is �xed and the angleincrement is varied.

The e�ect of the blurring artifact caused by the 30 mm polypropylene sphere in plane 4was quanti�ed for the di�erent cases. In �gure 8 the ASFs are plotted as a function of thedistance from plane 4. As can be seen in �gure 8A, the ASF is lowest for φ = 60◦ indicatingthat removal of out-of-plane blur decreases with increasing angular range. In �gure 8B, thereis a slightly lower ASF for ∆φ = 2◦ indicating blur decreases with a smaller angle incrementbetween each projection. Since the in�uence of quantum noise was sever when 31 projectionswere acquired it was not possible to compare the ASFs for case 3, when NAcq was varied.

3.2 Tomosynthesis compared to conventional X-ray imaging

3.2.1 Exposure

To compare tomosynthesis with conventional X-ray imaging the SDNR of the investigatedobjects have been plotted, see �gure 9. From these graphs it seems that SDNR increasesmuch more rapidly with exposure in the reconstructed images, though how this will a�ectthe visibility of objects is not clear.

Each of the projections were acquired with 60 kVp and di�erent mAs. Some of the recon-structed slices are shown in �gure 10 together with conventional images acquired with thesame tube settings. A higher mAs increases the SDNR more with tomosynthesis, as can beseen in �gure 9. In �gure 10 it is easier to discern small objects in the tomosynthesis imagescompared to the conventional, especially those in plane 4 (z = 120 mm above the table).Even though each of the studies were acquired with the same tube settings (same kV andtotal mAs) it must be kept in mind that the exposure will be a�ected by the inverse squarelaw due to the oblique tomosynthesis projections. Hence, to get comparable images (in termsof object visibility) a larger dose is required with the conventional technique.

3 RESULTS 14

0123456789

10

7 PMMA 10 PMMA 15 PMMA 10 Polyp. 15 Polyp. 20 Polyp.

Object

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60 deg./6 deg. 40 deg./4 deg. 20 deg./2 deg.

0123456789

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7 PMMA 10 PMMA 15 PMMA 10 Polyp. 15 Polyp. 20 Polyp.

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0123456789

10

7 PMMA 10 PMMA 15 PMMA 10 Polyp. 15 Polyp. 20 Polyp.

Object

SDN

R

60 deg. 40 deg. 20 deg.

A

B

C

Figure 7: The graphs show how the SDNR varies with A) tomographic angle, φ, B)angle increment, ∆φ, and C) number of projections, NAcq (∆φ = 2). Note (in A) thatobjects smaller than 15 mm were not visible when φ = 60◦.

3 RESULTS 15

0

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0 10 20 30 40 50 60 70 80 90Distance from the In-Focus slice (mm)

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Distance from the In-Focus slice (mm)

Art

ifac

t Sp

read

Fun

ctio

n

2 deg. 4 deg. 5 deg.

A

B

Figure 8: The artifact spread function as a function of the distance from plane 4 wherethe object is located. The parameter settings were; 60 kVp and 10 mAs/projection. InA) the angular range was varied (NAcq = 11) and B) the angle increment (φ = 40◦).

3 RESULTS 16

0

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32 64 128 252 400

mAs (total)

SDN

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Conventional Tomosynthesis

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B

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Figure 9: The SDNR variations with di�erent mAs settings for conventional X-rayimaging and tomosynthesis. The investigated objects were; A) a 10 mm polypropylenesphere located at plane 4, B) a 20 mm polypropylene sphere located at plane 1 andC) a 15 mm PMMA ellipsoid located at plane 1 of the physical phantom. In �gure 10the di�erent objects are marked with arrows.

3 RESULTS 17

32 mAs

Z = 30 mm

Z = 60 mm

Z = 90 mm

Z = 120 mm

Conv. images

128 mAs 400 mAs

A

BC

Figure 10: Slices reconstructed from 11 projections acquired with di�erent tubeloading and 60 kVp. Three di�erent exposures are shown together with images acquiredwith the conventional technique. Even though there are some artifacts present in thereconstructed slices the visibility of small objects is better in the slices especially thosein plane 4 (z = 120 mm above the table). The arrows indicate the objects that wereinvestigated.

3 RESULTS 18

3.2.2 Anthropomorphic phantom

The anthropomorphic phantom was reconstructed with 170 slices. The �ducial markers werelocated at zup = 150 mm (slice 135) and zlow = 50 mm (slice 48), which gave the distance∆z = 1.2 mm between two adjacent slices according to equation 8. Since the lung has athickness of approximately 150 mm in the AP direction, the entire lung was covered by ∼120slices.

a

d

c

b

e

Figure 11: Reconstructed tomosynthesis planes (a - d) of the anthropomorphic chestphantom and a conventional radiograph (e). The slices are reconstructed at; a) 41mm, b) 69 mm, c) 93 mm, d) 105 mm above the table. Each of the 11 tomosynthesisprojections and the conventional AP-projection were acquired with 100 kVp and 3.2mAs. In the reconstructed slices the ribs are blurred out and disappear when thedistance from the table increase (slices in the middle of the lung).

3 RESULTS 19

Tomosynthesis Conventional

Figure 12: The tomosynthesis image show a slice located 60 mm above the table.Some small structures that are obscured in the conventional AP image are broughtinto focus when the overlying ribs are removed (i.e. blurred out).

In �gure 11, reconstructed slices at di�erent depths are compared to a conventional chestradiograph. With tomosynthesis object visibility is increased when the window/level is op-timized for each individual slice. Another observation is that the ribs are removed (i.e.blurred out) and do not obscure objects in the middle of the lung, as they tend to do in theconventional image.

The visibility of the bronchus and some vascular structures is illustrated in �gure 12. Whenthe confusion of overlying anatomy is reduced in-focus objects are easier to discern. TheSDNR is higher in the reconstructed slice and the visibility of in-focus objects is also higher.Together with depth information from equation 8 the ability to locate (pathological) struc-tures will therefore increase with tomosynthesis compared to conventional planar X-ray im-ages.

4 DISCUSSION 20

4 Discussion

In this thesis we have investigated some of the fundamental parameters associated withthe acquisition and reconstruction in tomosynthesis. These parameters were optimized tocompare tomosynthesis with conventional X-ray imaging. A clinical comparison study wasalso performed using an anthropomorphic chest phantom.

Tomographic parameters

The results from the investigation of the tomographic parameters indicate that the angularrange (φ) has the greatest impact on image quality. The measured SDNR is generally lowerfor a larger φ and this is also possible to see in the images. A small angular range will improvethe clarity of the objects. Some of the smallest objects were not even visible in the imagesreconstructed from the φ = 60◦ projections. This is a result of the cone beam geometryand increasing mean path length of the photons resulting in a decreased photon �ux. Thisis also re�ected in the contrast of the in-focus slices, which becomes higher as the angularrange is reduced. When varying the number of projections acquired per series (with a �xedangular range) the visibility of the objects is fairly the same, independently on the numberof projections acquired. The reason for this is most likely due to the fact that each of thetomosynthesis series were acquired with the same total exposure, even though the dose perprojection was varied. With a smaller dose per projection the quantum noise will increase,but the dose did not vary enough to clearly visualize this e�ect.

The greatest advantage with tomosynthesis, compared to conventional X-ray imaging, isthe possibility to reduce the in�uence of over- and underlying structures from an arbitraryplane in the imaged volume. But since this reduction is performed by smearing the unwantedstructures over the interesting plane, the reconstructed images contain blur from out-of-planestructures. However, with the right parameter settings and reconstruction methods the blurcan be minimized, which would improve visualization of valuable diagnostic information.Therefore, the most important quality factor is the capability of tomosynthesis to reducethe blur. To quantify the out-of-plane blurring created from an object in a homogenousbackground, the artifact spread function was measured in images acquired with di�erentparameter settings. The graphs of the ASFs indicate that a large angular range minimizesthe blurring. Moreover, the ASF also quanti�es the capability of tomosynthesis to separatethe reconstructed planes. Hence, less blur from overlying structures can also be interpretedas an increase in Z-resolution. In �gure 6 this can be con�rmed by comparing the visibility ofthe 30 mm ellipsoid. It is di�cult to draw conclusions regarding the correlation between theprojection spacing, ∆φ, (or number of projections) and the blur from the graph of the ASFs(�gure 8), they are roughly the same. Intuitively, a decrease in ∆φ leads to an increase inNAcq and the exposure per projection must be adjusted accordingly (decreased to acquire thesame total exposure). Therefore, objects in the in-focus plane will have a signal proportionalto NAcq and out-of-plane objects will have a lower signal, proportional to 1/NAcq. Whenadding the projections, objects outside the in-focus slice will be repeated (or smeared) overthe image proportional to NAcq. Hence, a larger number of projections (small ∆φ) willminimize the in�uence of over- and underlying structures i.e. allow reconstruction with fewerartifacts.

4 DISCUSSION 21

Some of the key results from the investigation of the tomographic parameters are summarizedbelow.

• ↓ φ ⇒ ↑ SDNR (of in-focus objects) and ↓ Z-resolution

• ↓ NAcq ⇒ ↑ SDNR (of in-focus objects) and ↓ Z-resolution

• The blurring artifacts created from out-of-plane structures in the in-focus plane is acontinuous e�ect that depends on the distance between the planes

• Since the blurring artifact is a result of overlying structures that are not separated fromthe in-focus plane, blur decrease as Z-resolution increase

It is important to stress that these results are just a rule of thumb, the optimal parametersetting depends on the speci�c situation and the composition of the anatomical surrounding.However, to minimize the in�uence from over- and underlying structures, which is the bene�twith tomosynthesis, it is best to choose a large angular range with many projections. Theangular range and the number of projections must then be balanced against the fact thatfor a given total examination dose, more exposures will reduce the signal for each individualprojection. If the dose per projection is too low the image quality will be degraded due toreceptor noise. Therefore the tomographic parameters (and exposure) must be chosen so thatthe SDNR of the in-focus objects is su�cient to visualize the speci�c structures.

Tomosynthesis compared to conventional X-ray imaging

Images were acquired with the conventional technique using �ve di�erent tube loadings and�ve tomosynthesis series were performed with the same total tube loading. A fact that mustbe considered with �xed tube settings, kVp and mAs, is that the exposure will vary amongthe di�erent projections due to the inverse square law. The exposure is therefore slightlylower with tomosynthesis. At the lowest exposure level the noise is high and the contrastpoor, making the visibility of the smallest objects very low, for both of the modalities. Asthe exposure is increased the noise is reduced and objects in the in-focus slice becomesmuch easier to discern. Even though the exposure is fairly the same, the reconstructedtomosynthesis slices have a much better object visibility compared to the conventional images.The tomosynthesis images are even superior to conventional images acquired with a higherexposure. To improve the tomosynthesis investigation further, the dose per projection couldhave been weighted accordingly to the position of the tube. By using this approach thetotal exposure is more e�ciently divided, making the outermost projections less in�uencedof quantum noise.

The investigated objects are much easier to discern in the reconstructed slices, for all exposurelevels. The signal from an object in a speci�c plane is the sum of the signals from that objectin all of the projections. For a high contrast object, such as the bronchus in the lungs or thespheres and ellipsoids in the physical phantom, the visibility is higher with tomosynthesis.The structures outside the in-focus plane are repeated (blurred out) in the direction of thetube movement. This will retain the high-frequency information and greatly reduce thecontrast of out-of-plane structures. This is re�ected in that small objects becomes visible atlower exposure with tomosynthesis. Despite the artifacts in the reconstructed images, objectvisibility is clearly better with tomosynthesis even with a lower dose.

The study of the anthropomorphic chest phantom showed a clinical example of the ability tovisualize structures in 3 dimensions with tomosynthesis. In the anatomical images the blur

5 CONCLUSIONS 22

degrades the images and make the reconstructed slices fuzzy and not as crisp as the con-ventional image. Although, the 3D volume reconstructed with tomosynthesis had increasedvisibility of local structures. The reason for this is that the surrounding anatomy to anin-focus slice is smeared over the image instead of superimposed on the in-focus structures.Ribs that tend to obscure under-/overlying tissues were removed (i.e. e�ciently blurred out)in the reconstructed slices which increased the contrast for some obscured objects. Laterally,where the ribs curve, visibility was increased with tomosynthesis due to improved contrastbetween the underlying object and the blurred-out ribs. The visibility of the bronchus andsome vascular structures were increased with tomosynthesis due to the removal of overlyingstructures and the possibility to cut through them. Together with the depth informationtomosynthesis holds the potential to improve sensitivity of pulmonary lesions over conven-tional X-ray imaging. This would also improve early detection of subtle lung nodules whichwould decrease the need for recalls. It might even be possible to discriminate between be-nign and malignant lesions, since the reconstructed three-dimensional volume, rather thana two-dimensional radiograph, provides information on the dimension of the lesion, on thedistribution of the lesion and about the density of the lesion.

This study has focused on several parameters that a�ect image quality in tomosynthesisimages, namely total angular range, number of projections and angular increment. Thee�ects of these were compared using both physical measures such as SDNR as well as visualinterpretation of the images. Based on visual quality assessment, tomosynthesis imagesbene�t more from increases in dose than conventional images. Additionally, for the samedoses, tomosynthesis images show increased visibility of certain structures. To con�rm theseresults experimentally, which was beyond the scope of this thesis, clinical trials with humanobservers that compare images acquired with conventional X-ray images and tomosynthesismust be performed.

5 Conclusions

Compared to conventional X-ray imaging, tomosynthesis o�ers 3-dimensional informationwith increased clarity of in-focus objects due to reduced tissue overlap. The depth-resolutionof the in-focus structures can be optimized by the right choice of parameter settings, with theangular range and number of projections being the most essential. But to evaluate the clinicaldetection and diagnostic accuracy, clinical trials will be necessary with human observers incombination with case speci�c optimization of the parameter settings.

6 Acknowledgements

First of all I would like to thank my supervisor Anders Tingberg for giving me the greatopportunity of studying tomosynthesis and for all the help during the project. I wouldalso like to thank Mark Ruschin for immensely helpful comments, criticisms and suggestions.Another person that have contributed a great deal for making this project possible is MagnusBåth, who provided me with the reconstruction software, thank you.

During my project in Malmö I have met many people who all have been very helpful andcontributed in di�erent ways to the project. Among these, I specially thank Peter Wallenius

6 ACKNOWLEDGEMENTS 23

for introducing me to the operational software and helping me with other practical things, to-gether with interesting discussions. And �nally I would also like to thank Mikael Gunnarssonand Marcus Hultgren for helping me with the CT acquisition and reconstruction.

REFERENCES 24

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